Differential Equation question

The problems in the section of the book list the questions in this way:

dy/dx = 4y+e^4xsin(5x) and y(0)=1

First I get P(x)= -4 and then Q(x) = e^4x sin(5x)

then we put it in standard form and put the y on the left and the x on the right. Take the derivative first and then integrate. I understand the problems from #'s 18 on but the first 18 are set up like this:

y'-2xy= e^x^2 In the directions it states: primes denote derivatives with respect to x. The teacher explained the part in the book and with his example I understood and could do the later problems but I guess sometimes the hang up is what the question is asking. If someone has time to show me an example of the type y' -2xy= e^x^2 I would appreciate it. I assume we would do the same, get y on the left and x on the right and follow the same steps but not sure how to start. It seems that math is seeing patterns and if I could see one problem worked out I should be able to see the pattern and finish the rest of them.

Thank You,

Keith